ON EMBEDDINGS OF LOGARITHMIC BESSEL POTENTIAL SPACES

We present embedding theorems for certain logarithmic Bessel potential spaces modelled upon generalized Lorentz-Zygmund spaces and clarify t he role of the logarithmic terms involved in the norms of the space me ntioned. In particular, we get refinements of the Sobolev embedding th eorems, Trudinger's limiting embedding as well as embeddings of Sobole v spaces into space of lambda-Holder-continuous functions including th e result of Brezis and Wainger. (C) 1997 Academic Press.